Python實現 logistic 回歸算法

---

1、算法介紹

模型描述：

sigmoid函數：

原理： 優化目標：最小化 sigmoid(f(x)) 和真實標簽的差別（有不同的 cost function）。運用算法（梯度上升等）更新參數w、b。

---

2、Python代碼實現及注釋

決策邊界：

代碼：

import numpy as np from matplotlib import pyplot as plt# 加載數據集 def loadDataset(filename):# 數據集dataList = []# 數據樣本labelsList = []fr = open(filename)for line in fr.readlines():lineArr = line.strip().split()# 添加一個值為1的特征，對應于參數bdataList.append([1.0, float(lineArr[0]), float(lineArr[1])])labelsList.append(int(lineArr[-1]))return dataList, labelsList# sigmoid函數計算 def sigmoid(z):return 1.0/(1+np.exp(-z))# 運用標準的梯度上升法更新參數 def gradAscent(dataList, labelsList):dataMat = np.mat(dataList)labelsMat = np.mat(labelsList).Tm, n = np.shape(dataMat)learningRate = 0.1maxCycles = 1000weights = np.ones((n, 1))for i in range(maxCycles):a = sigmoid(dataMat*weights)# 梯度計算的公式error = labelsMat - a# 更新參數weights = weights + learningRate*dataMat.T*error/mreturn weights# 運用隨機梯度上升更新參數 def stocGradAscent(dataList, labelsList):m, n = np.shape(dataList)maxCycles = 200weights = np.ones(n)for j in range(maxCycles):for i in range(m):# 學習率遞減learningRate = 4/(1.0+j+i)+0.01# randIndex = int(np.random.uniform(0, m))# 計算 sigmoid 一次只計算一個樣本a = sigmoid(np.sum(dataList[i]*weights))error = labelsList[i] - aweights = weights + learningRate*error*np.array(dataList[i])return weights# 繪制數據集及決策邊界 def plotLine(dataSet, labels, weights):# 繪制數據集，不同類別顏色不同plt.scatter(np.array(dataSet)[:, 1], np.array(dataSet)[:, 2], 30 * (np.array(labels)+1), 15*np.array(labels))# 令表達式=0繪制決策邊界x = np.expand_dims(range(-3, 3, 1), 1)y = (-weights[0]-x*weights[1])/weights[2]plt.plot(x, y)plt.show()# 測試 logistic 回歸分類器 def predict(sample, weights):# 重構樣本特征向量sample = np.array([1.0, sample[0], sample[1]])prob = sigmoid(np.sum(sample*weights))if prob > 0.5:print("this is a positive")else:print('this is a negative')if __name__ == '__main__':# 加載數據集dataList, labelsList = loadDataset('testSet.txt')# 得到模型參數# weights = gradAscent(dataList, labelsList)weights = stocGradAscent(dataList, labelsList)print(weights)# 繪制決策邊界plotLine(dataList, labelsList, weights)# 測試分類器sample = np.array([1, 9])predict(sample, weights)

---

總結

以上是生活随笔為你收集整理的Python实现 logistic 回归算法的全部內容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網站內容還不錯，歡迎將生活随笔推薦給好友。